7. HEAT TRANSFER SPRING 2009
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1 7. HEA RANSFER SPRING 9 7. Diniion 7. Mo o a ranr 7.3 Pranl nmbr 7.4 Dimnionl nmbr in r an or onvion 7.5 nrg aion 7.6 Laminar bonar lar i iormal all 7.7 mrar roil in a rbln bonar lar 7.8 Ha-ranr oiin 7.9 mrar ingral rl 7. Enginring a-ranr allaion 7. Rrn Eaml 7. Diniion Ha ranr i nrg in rani o a mrar irn. a l i ra o a ranr r ni ara. 7. Mo o Ha ranr 7.. Conion Ha ranr o mollar aivi in abn o a blk moion. Forir La k k i onivi o a. A ºC, k ar.64 W m K ; k air.57 W m K. 7.. Avion Ha ranr o blk moion o li. i ii a aai a onan rr. i a rrn all rnal or r-ram mrar. A ºC, ar 48 J kg K ; air 7 J kg K. rbln Bonar Lar 7 - Di Al
2 7..3 Raiaion Ha ranr b miion o lromagni raiaion. San-Bolzmann La W m K 4 i San-Bolzmann onan. i miivi or a r blak bo 7..4 Fr an For Convion For li, onion an ion ar all ombin a onvion, i ma b ir: or onvion lo rivn b rnal man; r or naral onvion lo rivn b boan. A lo, bo ar rn an rr o mi onvion. Rgarl o onviv a-ranr manim i i ommon o ri Non la o ooling 4 i onviv a-ranr oiin; i ra mrar; i rram mrar rnal lo or blk mrar inrnal lo. 7.3 Pranl Nmbr Pranl nmbr Pr 5 k i raio o momnm iivi o a iivi k /. I i a mar o rlaiv ivn o momnm an nrg ranor b iion in vloi an rmal bonar lar. For air a normal mrar, Pr.7. For a laminar bonar lar: ga: Pr lii mal: Pr oil: Pr» «r an ar, rivl, ikn o momnm an rmal bonar lar. In gnral, / Pr. No a man li rori, noabl vioi, var baniall i mrar. In bonar-lar allaion i i ommon o vala m a ilm mrar, rag o r-ram an ra mrar: 6 rbln Bonar Lar 7 - Di Al
3 7.4 Dimnionl Nmbr in Fr an For Convion 7.4. Fr Convion rmal anion oiin. boan or r ni ma i g. 3 g L Grao nmbr: Gr 7 Raio o boan o vio or. I rol in r onvion i m am a a o Rnol nmbr in or onvion. Ralig nmbr: Ra g L 3 Gr. Pr For Convion L Nl nmbr: N 9 k Raio o aal o oniv a l Sanon nmbr: S N R.Pr Raio o aal o iv a l. In all a i i nar o i a lng, vloi an mrar al ar bing. For allaion, nginr rir an N or S. B imnional anali, N NR, Pr 7.5 Enrg Eaion nrg aion or li lo an b rin in an o onvnin orm: Inrnal nrg: D D a D D Enal : ρ D D b D oal nal : i ij ρ D ra o ranr o manial o a nrg i.. ra o orking o vio or i givn b i ij Sij S 3 kk ij j LHS o an o nrg aion an alo b rin in onrvaiv orm;.g. j rbln Bonar Lar 7-3 Di Al
4 D D For ial ga,, 3 v r v an ar ii a aaii a onan volm an onan rr, rivl. Ekr nmbr E 4 i raio o kini nrg o nal ang aro a lar an i all am mall n a ranr i o inr. A lo a ang in nrg or nal i roorional o a ang in mrar: nal P r ni ma 5 an n nrg aion an b rin a a mrar aion. inomribl bonar-lar aion or momnm an nrg ma b rin: P v v 6 v k v man vrial a l i: k v 7 o rbln i an aiional n a l o vrial migraion o li lmn arring ir on mrar or nrg onn. 7.6 Laminar Bonar Lar Wi Iormal Wall Sbiing Blai olion ino mrar aion giv Pr 8 r bonar-lar oorina η an imnionl ram nion η ar: 9 an θ i imnionl mrar in b,, mrar aion in bonar-lar oorina i rail olv in rm o Blai nion Eaml. olion, i i larl a nion o Pr, an b obain nmriall. rbln Bonar Lar 7-4 Di Al
5 o a goo aroimaion, / 3 an n N.33 Pr k R /. Pr Comaring i kin-riion rl or N R. Pr / 3.33 R / Pr /.664 R / 3, S / 3 Pr i i omim all Cilon-Colbrn ormla. Sin /, ingraing a l ovr a ini lng L an raging giv / / 3 N N L.664 R Pr 3 Again, omar momnm rl: L / L.38R L L. D 7.7 mrar Proil in a rbln Bonar Lar o rbln i an aiional vrial a l laion o aril arring ir mrar i m. v o all-normal In rbln or onvion on ol am ing moion o b ronibl or iing bo a an momnm o a A Rnol analog la o an -iivi mol: momnm: v a: v 4 r Pr omim 5 i rbln Pranl nmbr. Pr i a nion o mollar Pranl nmbr Pr, b all in lii mal Pr.9.. For momnm alra in a vloi al rom all ar r: 6 In lik mannr, or a ranr an in a mrar al rom all a l: 7 rbln Bonar Lar 7-5 Di Al
6 No a an ir ign. In all ni,, 8 In ovrla lar imnional anali giv onan rom i on ma rovr a logarimi roil. grain-ranr oi giv an, riing, Pr Pr n mrar la o all Pr Pr / or Pr Pr In nar-all limi /, Pr 3 In ovrla rgion / >>, Pr ln APr nion APr i riv b ingraion o 9. An a rv i or Pr.7 i 3 A Pr 3Pr / 7 3 b mor omlia rion bn givn Kar, 98. / Ha-ranr Coiin W obain kin-riion oiin ining momnm ranr b aming logarimi roil o al aro ar lar. An al analogo ni an b or a ranr. No a rl or la la an i lo blo ar ril or onan-mrar iormal all; varing all mrar ma b ra b an ingral anali Sion Ernal Flo Fla-Pla Bonar Lar Aling mrar an vloi la a bonar lar : rbln Bonar Lar 7-6 Di Al
7 Pr 3 ln A A 3Pr / 7 ln B B 5.,.45 Sbraing, aming Pr an /, A B Sbiing or in rm o a l giv P A B i an b rarrang o giv / S A B / / r S i Sanon nmbr. Sbiing or APr i giv P / S 33 / 3 3Pr 4 / Hovr, or ial aramr val i i ll-aroima b laminar rion - aion - an i i all imlr orm i i in allaion Inrnal Flo Pi Flo Sanon nmbr or i lo i in in rm o blk mrar, no nrlin mrar: S 34 r R R R r R r i ian o nar all. R r r Aming Pr, m algbra Eaml ion ro / S 35 / 3 3Pr / 7.4 / rbln Bonar Lar 7-7 Di Al
8 rbln Bonar Lar 7-8 Di Al 7.9 mrar Ingral Rl Wriing bonar-lar mrar aion in onrvaiv orm, v an braing im onini aion v giv v ] [ ] [ Ingraing rom o, aming imrmabl all, il 36 nal ikn δ i in b 37 Hn, rom abov, ] [ 38 Dirniaing ro, an iviing b i bom 39 r Sanon nmbr 4 ingral rlaion 39 ma b o riv oal a ranr in a r ra mrar an/or r-ram vloi ar anging. I ar onan, ovr, ingral rlaion r iml o 4 i obvio imilarii o orroning momnm ingral or.
9 7. Enginring Ha-ranr Callaion For raial nginring allaion ar ma i largl mirial orrlaion or Nl or Sanon nmbr in rm o R an Pr. For irlar linr, Crill an Brnin 977 roo / / 3 5 / 8.6 R Pr R D D N D.3 / 3 / 4 4 [.4 / Pr ] 8 r all li rori ar vala a ilm mrar. For orrlaion or man or gomri, inling b bnl,,.g. Inrora an D Wi, / 5 7. Rrn Crill, S.W. an Brnin, M., 977, J. Ha ranr, 99, 3. Inrora, F.P. an D Wi, D.P., 99, Inroion o Ha ranr, n E., Wil. Kar, B.A., 98, mrar an onnraion roil in ll rbln bonar lar, Inrna. J. Ha an Ma ranr, 4, rbln Bonar Lar 7-9 Di Al
10 Eaml Qion. a So a, or l-imilar laminar bonar-lar roil o orm in b a ramnion: r n normali mrar roil, A aii A Pr i giv Blai A an Falknr-Skan A /m bonar-lar olion a ial a. b So a olion in rm o i A Pr A Pr Qion. Calla Ekr nmbr E or air lo a m a a all i P mrar mainain a 5 ºC abov ambin. Qion 3. B aming logarimi man vloi an mrar roil ol rig o nr o a i, o a Sanon nmbr S in ll-vlo i lo i givn b / S / 3 3Pr / 7.4 / Qion 4. Air a ºC an am. lo a 6 m a a moo la la m long an.8 m i. la ra mrar i 5 ºC. Aming rbln lo rogo, ima oal ra o a lo rom on i o la. rbln Bonar Lar 7 - Di Al
11 Qion 5. Calla ra o a ranr r ni lng or a 5-mm-iamr linr mainain a a onan 6 ºC in an airram o mrar 5 ºC an vloi m. Anr kw 5 95 W m rbln Bonar Lar 7 - Di Al
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